Polynomial and Rational Functions: Structure and Behavior: Math Unit 2, Grade 12 (Letters & Devotion)

Description

Polynomial and Rational Functions: Structure and Behavior is Unit 2 of Precalculus: Functions, Trigonometry, and Mathematical Modeling (Grade 12), the Letters & Devotion Math course, complete in one printable PDF: 10 lessons, the unit check-up and the answer key, 70 pages.

• The relationship between factor multiplicity (odd vs even) and graph behavior at a zero
• The rule linking a polynomial’s degree parity and leading coefficient sign to its end behavior
• Synthetic division and the remainder theorem as tools for testing and extracting factors of a polynomial
• The complete zero-finding and multiplicity-based sketching process for a higher-degree polynomial function
• Why a vertical asymptote arises from division by a factor approaching zero
• The cancel-before-classify procedure for distinguishing holes from vertical asymptotes in a rational function
• The degree-comparison rule for horizontal asymptotes of rational functions, grounded in end-behavior reasoning
• The complete set of structural predictors (multiplicity, leading term, degree comparison, cancellation) that jointly determine a polynomial or rational function’s graph
• The inverse construction problem: building a rational function’s algebraic form from specified zero, asymptote, and hole behavior
• Unit 1’s function-family identification vocabulary, applied to novel equations mixed with this unit’s content

Every lesson is written for a parent with no teaching background: it opens with a short script to read aloud, names the specific wrong idea a student is likely to reach for and how to correct it, and closes with a practice sheet you may copy for your household. Scripture references are King James Version throughout. Black-and-white, 8.5 x 11 in. The whole year of this course is also in this store as a single book.

AI note: The written content of this resource was drafted with AI tools, then reviewed and edited by the author.